Scattering and a Plancherel formula for real reductive spherical spaces
Abstract
We establish the analog for real homogeneous spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh (Periods and harmonic analysis on spherical varieties, Asterisque 396, (2017), Theorem 7.3.1) for p-adic wavefront spherical varieties. We use properties of the Harish-Chandra homomorphism of Knop for invariant differential operators of the variety, special coverings of the variety and spectral projections. Our main result depend on an analog of the Discrete Series Conjecture of Sakellaridis and Venkatesh (\cite{SV}, Conjecture 9.4.6). Their result quoted above depends on this Discrete series conjecture.
Cite
@article{arxiv.2305.13867,
title = {Scattering and a Plancherel formula for real reductive spherical spaces},
author = {Patrick Delorme},
journal= {arXiv preprint arXiv:2305.13867},
year = {2026}
}
Comments
99 pages. Some errors or gaps repaired in sections 3.4, 3.5. Some changes in Lemmas 8.9, 8.10. Accepted in Compositio Mathematica